Let `x = 597 xx 10 ^(22) + 73.5 xx 10 ^(21)` when x is expressed in standard form as `6.0435 xx 10^(m),` then the value of m is

Options

A. 22
B. 23
C. 24
D. 21

Answer

To solve the problem, we need to express \( x = 597 \times 10^{22} + 73.5 \times 10^{21} \) in standard form as \( 6.0435 \times 10^{m} \) and find the value of \( m \).

### Step-by-Step Solution:

1. **Identify the terms**: We have two terms in the expression:
- \( 597 \times 10^{22} \)
- \( 73.5 \times 10^{21} \)

2. **Convert the second term**: To combine these two terms, we can express \( 73.5 \times 10^{21} \) in terms of \( 10^{22} \):
\[ 73.5 \times 10^{21} = 73.5 \times 10^{21} \times \frac{10}{10} = 7.35 \times 10^{22} \]

3. **Combine the terms**: Now we can add the two terms together:
\[ x = 597 \times 10^{22} + 7.35 \times 10^{22} = (597 + 7.35) \times 10^{22} = 604.35 \times 10^{22} \]

4. **Convert to standard form**: To express \( 604.35 \) in standard form, we need to write it as \( 6.0435 \times 10^{n} \). We can do this by moving the decimal point one place to the left:
\[ 604.35 = 6.0435 \times 10^{2} \]
Therefore, we can rewrite \( x \):
\[ x = 6.0435 \times 10^{2} \times 10^{22} \]

5. **Combine the powers of ten**: When multiplying powers of ten, we add the exponents:
\[ x = 6.0435 \times 10^{(2 + 22)} = 6.0435 \times 10^{24} \]

6. **Identify \( m \)**: From the expression \( 6.0435 \times 10^{m} \), we see that \( m = 24 \).

### Final Answer:
The value of \( m \) is \( 24 \).